8/17/2019 11 Divisibility Rules and Prime Factorization Notes

1/24

1 1 D i v i s i b i l i t y R u l e s a n d P r i m e F a c t o r i z a t i o nC h a p t e r s 5 . 1 - 2 , D a t e _ _ _ _ _      

2      i f t h e n u m b e r i s e v e n      

3      i f t h e s u m o f i t s d i g i t s i s d i v i s i b l e b y 3      

5 i f t h e l a s t d i g i t i s 0 o r 5      

1 0      i f t h e l a s t d i g i t i s 0      

8/17/2019 11 Divisibility Rules and Prime Factorization Notes

2/24

  5 4 0 7 5 2 2 3 3 1 4 5 , 2 1 5      

2   

3   

5   

1 0   

8/17/2019 11 Divisibility Rules and Prime Factorization Notes

3/24

  5 4 0 7 5 2 2 3 3 1 4 5 , 2 1 5      

2   

3   

5   

1 0   

8/17/2019 11 Divisibility Rules and Prime Factorization Notes

4/24

  4 8 0 4 5 9 6 7 5 5 6 , 3 6 0      

2   

3   

5   

1 0   

8/17/2019 11 Divisibility Rules and Prime Factorization Notes

5/24

  4 8 0 4 5 9 6 7 5 5 6 , 3 6 0      

2   

3   

5   

1 0   

8/17/2019 11 Divisibility Rules and Prime Factorization Notes

6/24

F i n d i n g F a c t o r s    

A n a t u r a l n u m b e r i s f a c t o r e d w h e n i t i s w r i t t e n

a s t h e p r o d u c t o f t w o o r m o r e n a t u r a l n u m b e r s .

 N a t u r a l n u m b e r s a r e t h e c o u n t i n g n u m b e r s : 1 ,

2 , 3 , 4 , e t c .  

F o r i n s t a n c e , 3 2 c a n b e f a c t o r e d a s 4 8 . T h en u m b e r s 4 a n d 8 a r e f a c t o r s o f 3 2 .  

8/17/2019 11 Divisibility Rules and Prime Factorization Notes

7/24

H o w d o w e l i s t a l l o f t h e f a c t o r s f o r 2 4 ?      

8/17/2019 11 Divisibility Rules and Prime Factorization Notes

8/24

H o w d o w e l i s t a l l o f t h e f a c t o r s f o r 2 4 ?      

8/17/2019 11 Divisibility Rules and Prime Factorization Notes

9/24

L i s t a l l o f t h e f a c t o r s f o r 3 6 .  

8/17/2019 11 Divisibility Rules and Prime Factorization Notes

10/24

L i s t a l l o f t h e f a c t o r s f o r 3 6 .  

8/17/2019 11 Divisibility Rules and Prime Factorization Notes

11/24

L i s t a l l o f t h e f a c t o r s f o r e a c h n u m b e rf r o m l e a s t t o g r e a t e s t .  

A . 1 5      

B . 4 0      

C . 4 5      

D . 6 4      

8/17/2019 11 Divisibility Rules and Prime Factorization Notes

12/24

L i s t a l l o f t h e f a c t o r s f o r e a c h n u m b e rf r o m l e a s t t o g r e a t e s t .  

A . 1 5      

B . 4 0      

C . 4 5      

D . 6 4      

8/17/2019 11 Divisibility Rules and Prime Factorization Notes

13/24

 A n a t u r a l n u m b e r i s p r i m e        i f i t h a s e x a c t l y t w o

f a c t o r s , i t s e l f a n d 1 .  

E x a m p l e s : 2 , 3 , 5 , 7 , 1 1 , 1 3 , . . .  

 A n a t u r a l n u m b e r i s      c o m p o s i t e i f i t h a s t h r e e o r

m o r e f a c t o r s .  

E x a m p l e s : 4 , 6 , 8 , 9 , 1 0 , 1 2 , . . .  

8/17/2019 11 Divisibility Rules and Prime Factorization Notes

14/24

I s t h e n u m b e r p r i m e o r c o m p o s i t e ?      

1 3      p r i m e      

2 6      c o m p o s i t e      

2 9      p r i m e      

1     n e i t h e r    

8/17/2019 11 Divisibility Rules and Prime Factorization Notes

15/24

F a c t o r T r e e s      

U s e f a c t o r t r e e s t o f a c t o r a n u m b e r u n t i la l l o f i t s f a c t o r s a r e p r i m e .  

2 8   

8/17/2019 11 Divisibility Rules and Prime Factorization Notes

16/24

W r i t e t h e p r i m e f a c t o r i z a t i o n o f 4 0 .  

4 0   

8/17/2019 11 Divisibility Rules and Prime Factorization Notes

17/24

W r i t e t h e p r i m e f a c t o r i z a t i o n o f 4 0 .  

4 0   

8/17/2019 11 Divisibility Rules and Prime Factorization Notes

18/24

W r i t e t h e p r i m e f a c t o r i z a t i o n o f e a c h n u m b e r .  

1 6      1 2 5   

8/17/2019 11 Divisibility Rules and Prime Factorization Notes

19/24

W r i t e t h e p r i m e f a c t o r i z a t i o n o f e a c h n u m b e r .  

1 6      1 2 5   

8/17/2019 11 Divisibility Rules and Prime Factorization Notes

20/24

U s e a f a c t o r t r e e t o w r i t e t h e p r i m e

f a c t o r i z a t i o n o f e a c h n u m b e r .  

E .    4 2      F      .    6 0   

8/17/2019 11 Divisibility Rules and Prime Factorization Notes

21/24

U s e a f a c t o r t r e e t o w r i t e t h e p r i m e

f a c t o r i z a t i o n o f e a c h n u m b e r .  

E .    4 2      F      .    6 0   

8/17/2019 11 Divisibility Rules and Prime Factorization Notes

22/24

U s e a f a c t o r t r e e t o w r i t e t h e p r i m e

f a c t o r i z a t i o n o f e a c h n u m b e r .  

G .    3 6 H       . 7 5   

I .    2 1     J .    2 0 0   

8/17/2019 11 Divisibility Rules and Prime Factorization Notes

23/24

U s e a f a c t o r t r e e t o w r i t e t h e p r i m e

f a c t o r i z a t i o n o f e a c h n u m b e r .  

G .    3 6 H       . 7 5   

I .    2 1     J .    2 0 0   

8/17/2019 11 Divisibility Rules and Prime Factorization Notes

24/24